Megan McArdle has a good post and excerpts from Adam Shepard, who set out with $25 to see how hard it was to escape from poverty. I won't re-quote that post here, you should see her site, but I wanted to comment on one thing Shepard says about his early days trying to convince supervisors they should hire a homeless guy:

So, he gave me the secret. To paraphrase, he told me to go to these
managers and tell them who you are, that you are the greatest worker on
the planet and that it would be a mistake not to hire you. If they take
you on, great. If not, move on down the line. By day's end, you're
gonna have a job.

So I did. The next day, I went to see Curtis at Fast Company, a
moving company where I'd already applied. "Curt!" I said. "I'm Adam
Shepard, and I'm the greatest mover on the planet. It would be a
mistake for you not to hire me." He looked at me across the table and
smiled, knowing I was lying like hell to him. But he liked my attitude
"“ especially after I offered to work a day for free "“ so he hired me on
the spot.

This is very normal -- if you want someone to take a risk, you try to reduce the cost for him. Not sure you want to try our product? We'll give you a free sample. In this case, he agreed to work for free to convince the manager he was a good worker. This makes sense -- to emerge from homelessness and to get a job with no skills and no work history, one needs to be willing to give a bit of a discount on your labor, at least at first, to get someone to give you a chance.

But here is the interesting part -- the arrangement Curtis and Adam Shepard made is ILLEGAL. The Fair Labor Standards Act, which includes Federal minimum wage law, does not allow Curtis to accept unpaid labor and does not even allow Mr. Shepard to offer it. The fact that the deal makes so much sense and it so clearly is in the mutual best interest of both parties is absolutely irrelevant under the law. Fast Company could be busted, should the DOL choose to focus its attention their way.

When people argue that the minimum wage is most harmful to the poor, because it prices the first rung of the labor ladder beyond what their minimal skills can justify, this is what they mean.